第42卷第3期2023年3月硅㊀酸㊀盐㊀通㊀报BULLETIN OF THE CHINESE CERAMIC SOCIETY Vol.42㊀No.3March,2023冻融循环后PVA-ECC 拉伸性能衰减规律研究高秀梅1,刘曙光2,闫㊀敏3(1.内蒙古工业大学土木工程学院,呼和浩特㊀010000;2.内蒙古工业大学矿业学院,呼和浩特㊀010000;3.鄂尔多斯应用技术学院土木工程系,鄂尔多斯㊀017000)摘要:为研究聚乙烯醇纤维水泥基复合材料(PVA-ECC)冻融后的拉伸性能,分别对PVA-ECC 试件冻融0㊁25㊁50㊁75㊁100㊁125㊁150次后进行拉伸试验,通过试件表面特征和拉伸特征参数综合评价PVA-ECC 冻融后的拉伸性能,并采用向量自回归滑动平均(VARMA)模型探索冻融循环后拉伸特征参数之间的规律㊂结果表明,冻融循环试验后,试件均出现不同程度的损伤,损伤程度随冻融循环次数增加逐渐增大㊂初裂强度与抗拉强度随冻融循环次数的增加逐渐降低,拉伸应变与应变能随冻融循环次数的增加呈先升高后降低的趋势㊂基于试验数据建立了拉伸特征参数的关系式,进一步揭示了冻融循环后拉伸特征参数的衰减规律㊂关键词:聚乙烯醇纤维水泥基复合材料;初裂强度;抗拉强度;拉伸应变;应变能;冻融循环;衰减规律;VARMA 模型中图分类号:TU525.9㊀㊀文献标志码:A ㊀㊀文章编号:1001-1625(2023)03-0837-08Attenuation Law of Tensile Property of PVA-ECC after Freezing-Thawing CyclesGAO Xiumei 1,LIU Shuguang 2,YAN Min 3(1.School of Civil Engineering,Inner Mongolia University of Technology,Hohhot 010000,China;2.School of Mining Technology,Inner Mongolia University of Technology,Hohhot 010000,China;3.Department of Civil Engineering,Ordos Institute of Technology,Ordos 017000,China;)Abstract :In order to study the tensile property of polyvinyl alcohol fiber-reinforced engineered cementitious composite (PVA-ECC)after freezing-thawing cycles,the tensile tests were carried out on PVA-ECC specimens with 0,25,50,75,100,125,150freezing-thawing cycles.The tensile property of PVA-ECC after different freezing-thawing cycles was comprehensively evaluated by surface characteristic and tensile characteristic parameter.In addition,the vector autoregressive moving average (VARMA)model was used to explore the law of tensile characteristic parameter after freezing-thawing cycles.The results show that after freezing-thawing cycles,the specimens are all damaged to varying degrees,and the damage degree gradually increases with the increase of freezing-thawing cycles.The initial crack strength and tensile strength become smaller with the increase of freezing-thawing cycles,and the tensile strain and strain energy increase first and then decrease with the increase of freezing-thawing cycles.Based on the experimental data,some formulas relating to tensile characteristic parameter are proposed,which further reveal the attenuation law of tensile characteristic parameter after freezing-thawing cycles.Key words :polyvinyl alcohol fiber-reinforced engineered cementitious composite;initial crack strength;tensile strength;tensile strain;strain energy;freezing-thawing cycle;attenuation law;VARMA model收稿日期:2022-10-30;修订日期:2022-12-21基金项目:内蒙古自然科学基金(2020MS05016)作者简介:高秀梅(1994 ),女㊂主要从事复合材料力学性能方面的研究㊂E-mail:1172840138@通信作者:闫㊀敏,副高级工程师㊂E-mail:396446112@0㊀引㊀言为了弥补混凝土脆性差的短板,研究者[1-4]研制了纤维水泥基复合材料(engineered cementitious838㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷composite,ECC),该材料实现了单轴拉伸应变达到3%以上[5-7],有效解决了混凝土的脆性开裂问题[8]㊂然而,聚乙烯醇纤维水泥基复合材料(polyvinyl alcohol fiber-reinforced engineered cementitious composite,PVA-ECC)在服役期间多处于低温环境中,冻融作用会极大地加速PVA-ECC 性能劣化进程[9-10]㊂因此,开展PVA-ECC 冻融后拉伸性能试验研究,具有一定的价值和意义㊂自PVA-ECC 问世至今,众多学者围绕其制备方法[11]㊁力学性能[12-13]㊁构件性能[14]以及耐久性能[15]展开了研究,也取得了非常显著的成果㊂近些年来,PVA-ECC 已经被应用于许多实际工程中,美国密歇根州的无伸缩缝桥面是采用PVA-ECC 制作的桥面连接板[16],日本广岛县的Mitaka 水坝损坏后使用PVA-ECC 进行了修复[17],中国杭州萧山机场跑道同样使用了PVA-ECC 进行修复[18]㊂但是目前对于冻融后试件的拉伸性能试验研究相对较少,一方面是因为冻融循环作用后,拉伸试验结果存在较大误差;另一方面是因为冻融循环使这项试验周期变长㊂因此,本文进行0㊁25㊁50㊁75㊁100㊁125㊁150次冻融循环后的拉伸试验,通过试件表面特征和拉伸特征参数综合评价PVA-ECC 冻融后的拉伸性能,并以拉伸试验的特征参数为样本,引入向量自回归滑动平均模型,建立了冻融循环后拉伸特征参数衰减规律模型㊂1㊀实㊀验1.1㊀原材料采用P㊃O 42.5R 普通硅酸盐水泥,砂选用106~212μm 优质石英砂,粉煤灰选用一级高钙粉煤灰,减水剂采用高性能聚羧酸减水剂,水为实验室普通用水,所用聚乙烯醇纤维长度为12mm㊂其中聚乙烯醇纤维性能如表1所示㊂表1㊀聚乙烯醇纤维性能Table 1㊀Performance of polyvinyl alcohol fiberFineness /[g㊃(10000m)-1]Density /(g㊃cm -3)Diameter /μm Elongation /%Length /mm Tensile strength /MPa Elastic modulus /GPa 15 1.3406121600401.2㊀配合比本试验以冻融循环次数为研究变量,共设计七组试验㊂试验编号为Ft-0㊁Ft-25㊁Ft-50㊁Ft-75㊁Ft-100㊁Ft-125㊁Ft-150,编号中数字与冻融循环次数一致,其中Ft-0组为对照组㊂试验配合比为:水泥254kg /m 3,水305kg /m 3,石英砂457kg /m 3,粉煤灰1017kg /m 3,减水剂5.08kg /m 3,纤维26kg /m 3㊂1.3㊀试验方法图1㊀哑铃型试件形状及尺寸Fig.1㊀Shape and size of dumbbell-shaped specimen 拉伸试验参考日本土木工程学会(JSCE)推荐的方法[19],采用尺寸为330mm ˑ60mm ˑ13mm 哑铃型试件(见图1)㊂试件标距段用半径为61mm 的圆弧自然过渡到加载加持段,尽量避免试件在非标距段内出现裂缝或破坏㊂各组试件均自然养护28d,然后采用长春科新试验仪器有限公司生产的200kN 电子万能试验机(WDW-200)进行单轴拉伸试验㊂冻融试验按照‘普通混凝土长期性能和耐久性能试验方法标准“(GB /T 50082 2009)快速冻融,试验设备为济南思明特科技有限公司生产的冻融循环试验机㊂2㊀结果与讨论2.1㊀冻融循环试验结果及分析冻融试验前后PVA-ECC 试件的表面特征如图2所示㊂由图2可知,对照组试件表面较为平整光滑,存在少量成型过程气体逸出后留下的孔洞㊂经过冻融试验后,各试验组试件表面出现不同面积和剥落程度的第3期高秀梅等:冻融循环后PVA-ECC 拉伸性能衰减规律研究839㊀图2㊀冻融试验前后PVA-ECC 试件的表面特征Fig.2㊀Surface characteristics of PVA-ECC specimens before and after freezing-thawing tests 损伤㊂与Ft-100组和Ft-150组试件相比,Ft-50组试件表面仅表现出轻微剥蚀破损,冻融损伤程度最轻㊂随着冻融循环次数增加,试件表面的损伤面积越大,程度愈严重㊂其中Ft-150组试件损伤面积最大,表面剥落程度最高,裸露的纤维数目最多㊂2.2㊀单轴拉伸试验结果及分析图3为冻融试验前后PVA-ECC 试件拉伸破坏形态㊂可以看出,Ft-0组试件在拉伸过程中呈多重开裂模式㊂随着冻融循环次数增加,破坏过程中裂缝的宽度越来越窄,且数目越来越少㊂特别地,Ft-150组试件破坏之前几乎观测不到裂纹的产生与发展㊂经过0㊁25㊁50㊁75㊁100㊁125㊁150次冻融循环试验后,拉伸应力-应变曲线如图4所示㊂由图4可以看出,Ft-0组试件符合PVA-ECC 单轴拉伸典型应力-应变曲线特征,依次经历线弹性㊁弹塑性㊁应变硬化和破坏阶段,并且呈多重裂纹开裂现象㊂随着冻融循环次数增加,应力-应变曲线不再呈预示新裂缝产生的波动现象,曲线越来越光滑,弹塑性阶段延长,应变硬化开始阶段对应的应力降低,应变硬化结束阶段对应的应变先增加后降低,爬坡幅度变低㊂特别地,当冻融循环次数达到75次,拉伸应力-应变曲线呈平滑状;冻融循环次数为150次时,虽然极限应变仍大于3%,但曲线的四阶段分界点较为模糊㊂图3㊀冻融试验前后PVA-ECC 试件拉伸破坏形态Fig.3㊀Tensile failure patterns of PVA-ECC specimens before and after freezing-thawingtests 图4㊀冻融循环试验前后PVA-ECC 试件拉伸应力-应变曲线Fig.4㊀Tensile stress-strain curves of PVA-ECC specimens before and after freezing-thawing tests基于拉伸应力-应变曲线,得到了表征拉伸性能的特征参数,包括初裂强度㊁抗拉强度㊁拉伸应变㊁应变能(对应极限应力点的应力-应变曲线包含的面积)及对应的变化率(为便于对比分析,所有参数的提升率均基于对照组试件进行计算),分别显示于图5(a)~(d)㊂由图5(a)可知,当冻融循环次数为25㊁50㊁75㊁100㊁125㊁150次时,PVA-ECC 试件的初裂强度分别降低了45%㊁43%㊁74%㊁79%㊁82%㊁89%㊂可见,经过冻融循环后,PVA-ECC 试件的初裂强度呈阶梯式下降,第一梯度的冻融循环次数为25㊁50次,第二梯度的冻融循环次数为75㊁150次㊂分析原因,纤维增强水泥基复合材料的初裂强度主要由基体性能决定[20],而孔隙中的水分冻结后产生冻胀力,破坏了基体的内部结构,从而降低了试件的初裂强度,且损伤是由试件表面开始向内部蔓延,损伤程度随着循环次数的增多逐渐加重㊂从图5(b)可以得知,当冻融循环次数为25㊁50㊁75㊁100㊁125㊁150次时,PVA-ECC 试件的抗拉强度分别降低了11%㊁24%㊁28%㊁46%㊁48%㊁57%㊂说明PVA-ECC 的抗拉强度随着冻融循环次数的增加呈直线下降㊂已有研究[21]结果表明,纤维-基体界面黏结性能对纤维增强复合材料体系的抗拉强度有重要影响,且纤维与840㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷基体的界面黏结力主要由化学黏结力和摩擦黏结力组成[22]㊂冻融循环试验削弱了界面黏结力,从而导致体系抗拉强度的降低㊂图5㊀不同冻融循环后PVA-ECC 试件的初裂强度㊁抗拉强度㊁拉伸应变和应变能Fig.5㊀Initial crack strength,tensile strength,tensile strain and strain energy of PVA-ECC specimens after different freezing-thawingcycles 图6㊀不同冻融循环后PVA-ECC 试件的σ/σp 值Fig.6㊀σ/σp values of PVA-ECC specimens after different freezing-thawing cycles 由图5(c)可以看出,各试验组的拉伸应变随着冻融循环次数增加呈先增加后降低的趋势㊂与未冻融试件相比,经历不同冻融循环次数的试验组,其拉伸应变呈上升趋势,增加率分别为24%㊁64%㊁41%㊁40%㊁20%和12%㊂说明冻融对PVA-ECC 试件的拉伸极限应变产生有利影响,但是提高率呈先增加后降低的趋势㊂究其原因,基体性能和纤维-基体的界面黏结性能均是影响材料应变硬化行为的重要因素,因此可采用抗拉强度σ与初裂强度σp 的比值(σ/σp )表征拉伸应变性能的变化㊂不同冻融循环后PVA-ECC 试件的σ/σp 的变化规律如图6所示㊂所有试件的σ/σp 均超过了1(满足多缝开裂机制应力准则[23-24]),这很好地解释了试件表现出的应变硬化行为㊂与未冻融试件相比,经历不同冻融循环次数的试验组的σ/σp 提高率均大于0%,但是,当冻融循环次数达到75次时,试件的σ/σp 跃升至4.5,此时试件拉伸应变的提高率开始下降㊂由此说明,冻融循环试验后,若想获得理想的应变硬化行为,应该选择合理的σ/σp ,这一比值一般在2.0~2.5㊂通过图5(d)可以观察到,各试验组的应变能随着循环次数的增加呈先增加后降低的趋势,与拉伸应变性能变化规律相似㊂其中,提升率最高为6%,应变能为163.7kJ /m 3;减少率最大为61%,应变能为㊀第3期高秀梅等:冻融循环后PVA-ECC拉伸性能衰减规律研究841 60.3kJ/m3㊂这在一定程度上说明了冻融不利于PVA-ECC应变能的提高㊂造成PVA-ECC应变能较低的主要原因在于初裂强度和抗拉强度的下降速率远大于拉伸应变的增大速率㊂3㊀冻融后拉伸特征参数衰减模型与误差分析3.1㊀基于向量自回归滑动平均(VARMA)方法的衰减模型3.1.1㊀VARMA模型简介向量自回归模型(vector autoregressive model,VAR)是多元时间序列分析中的一种经典模型,为了提升它的建模能力[25],在向量自回归模型的基础上提出了一系列变种模型(variants)[26-27]㊂其中,向量自回归滑动平均(vector autoregressive moving average)[28]模型便是非常重要的一种,它融合了滑动平均,使模型本身拥有更丰富的参数化过程和更强的时间序列建模能力㊂另外,它也能对时间序列数据中的噪声进行平滑处理㊂模型的一般表达式如式(1)[29]所示㊂X t=ðd k+1A k x t-k+ðq p=1B pεt-p+u t㊀tɪ[1,T](1)式中:t表示时刻点,与冻融循环次数有关,本文中采用快速冻融方法,3h完成一次冻融循环,故而将冻融循环次数转化为时间数列;X表示因变量;x t-k表示t-k时刻的自变量;k表示自变量中过去时间点变量,初始值为0;A kɪR NˑN,其中A k表示系数矩阵,R NˑN表示NˑN维的实数矩阵;d表示自变量中当前时间点关联过去时间点的数量;εt-pɪR N,ε表示残差,R N表示1ˑN维的实数矩阵;p表示残差中过去时间点变量,初始值为1;B pɪR NˑN,B p表示系数矩阵;q表示残差中当前时间点关联过去时间点的数量;u t表示t时刻白噪声数值;T表示最终时刻㊂3.1.2㊀时间序列平稳化在建立VARMA(p,q)模型前,需要先判断各变量时间序列的平稳性㊂自相关图观察法和单位根检验法是检验平稳性的两种常用方法,其中自相关图观察法虽然操作简单,但不够严格[30]㊂为了保证模型的精度和可靠度,本文采用单位根检验(augmented dickey-fuller test,ADF)法对拉伸特征参数序列进行平稳性检验[31]㊂首先从图5可以直观地看出复合胶凝材料的拉伸特征参数均随冻融循环次数的增长而不断降低,需进一步检验其平稳性㊂将各冻融循环次数下复合胶凝材料的拉伸特征参数作单位根检验,结果列于表2㊂表2中,序列号1㊁2㊁3和4,分别代表拉伸应变㊁初裂强度㊁抗拉强度和应变能,原拉伸特征参数时间序列的T值的绝对值均小于1%㊁5%㊁10%水平的绝对值,故在三个水平下均可拒绝原假设㊂由表2可以看出,原始序列的p值均小于0.5,也证明原始序列平稳㊂故差分阶数d 的数值可取0㊂表2㊀拉伸特征参数序列ADF检验结果Table2㊀ADF test results of tensile characteristic parameter sequenceSerial number Difference order T p Critical value1%5%10% 10-1.7070270.427495-6.02511-3.829282-2.986710 20-2.0771700.253792-6.04511-3.929273-2.986810 30-1.3192610.420314-6.03511-3.929280-2.986810 40-2.6802060.489434-5.354256-3.646238-2.9011973.1.3㊀模型参数确定结合赤池信息准则(akaike information criterion,AIC)和贝叶斯信息准则(bayesian information criterion, BIC)来确定最优模型㊂AIC值和BIC值越小,拉伸特征参数选择就越精确,拟合效果也越好[32]㊂当p值等于5,q值等于0时,AIC值为-230.06,BIC值最小为-215.14㊂综合AIC值㊁BIC值和模型误差,最终确定极限点应变应用序列模型VARMA(5,0)㊂同理,将拟合的其余拉伸特征参数的VARMA(p,q)模型结果列于表3㊂根据模型参数进行表达式参数的计算,得到拉伸应变㊁初裂强度㊁抗拉强度和应变能模型表达式如式(2)~(5)所示㊂842㊀水泥混凝土硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷Y t =4.032-4.201y t -1+1.624y t -2-1.338y t -3+1.026y t -4+u t (2)Y t =3.103-3.683y t -1+1.500y t -2+1.235y t -3-1.023y t -4+u t (3)Y t =3.180-2.602y t -1-0.990y t -2+1.320y t -3-0.988y t -4+u t (4)Y t =2.107-1.293y t -1-1.551y t -2-0.932y t -3+0.995y t -4+u t(5)表3㊀不同冻融循环后PVA-ECC 的模型参数Table 3㊀Model parameters of PVA-ECC after different freezing-thawing cycles Serial number AIC BIC VARMA(p ,q )1-230.06-215.14(5,0)2-587.01-534.02(5,0)3-478.95-471.65(6,0)4-668.19-788.14(6,0)3.2㊀模型误差与分析图7㊀拉伸特征参数的残差分布图Fig.7㊀Residuals distribution plot of tensile characteristic parameter 以极限点应变序列模型VARMA(5,0)为例,对其进行残差检验㊂本文的复合胶凝材料冻融后拉伸特征参数衰减模型的残差应为没有任何规律的白噪声序列㊂若模型的残差不是白噪声序列,证明模型的拟合度不高,序列里有VARMA 模型无法解释的变异数据[33]㊂拉伸特征参数的残差分布图见图7,可以看出,残差分布的核密度估计曲线(KDE)接近正态分布曲线(N),故可以确定本文中使用的模型残差序列之间是相互独立的,是白噪声,初步判定该模型已包含原始序列的所有特征[34]㊂经检验,其他拉伸特征参数的模型残差也均为白噪声序列,满足要求㊂本文采用平均绝对百分比误差对VARMA(p ,q )进行误差分析㊂平均绝对百分比误差可以反映实际预测误差的大小,有效避免正负误差相互抵消的问题[35]㊂各试验组拉伸特征参数冻融循环VARMA(p ,q )模型参数值以及模型平均绝对百分比误差如表4所示,可以看出复合胶凝材料拉伸特征参数序列建立的模型绝对百分比误差较小,均小于7%,综合残差检验和误差分析说明,VARMA(p ,q )模型在预测PVA-ECC 冻融后的拉伸特征参数衰减规律方面具有较高精度㊂表4㊀各试验组VARMA (p ,q )模型参数值以及模型平均绝对百分比误差Table 4㊀VARMA (p ,q )model parameters and mean absolute percentage errors of each experimental groupSerial number 1234VARMA(p ,q )(5,0)(5,0)(6,0)(6,0)Mean absolute error /%0.0140.0680.0420.0634㊀结㊀论1)通过冻融循环试验发现,试件损伤程度随着冻融循环次数的增加逐渐增大,并且这种损伤是由试件表面开始,逐渐深入材料内部㊂2)通过冻融循环后的拉伸试验得到冻融循环后拉伸特征参数的变化规律㊂随着冻融循环次数增加,初裂强度呈阶梯式下降的趋势,降低率最大为89%,最小为45%;抗拉强度呈直线下降的趋势,降低率最大为57%,最小为11%;拉伸应变和应变能呈先增加后降低的趋势㊂3)采用VARMA(p ,q )模型对PVA-ECC 试件冻融循环后的拉伸特征参数进行分析,得到拉伸特征参数衰减规律的关系式㊂㊀第3期高秀梅等:冻融循环后PVA-ECC拉伸性能衰减规律研究843参考文献[1]㊀LI V C.高延性纤维增强水泥基复合材料的研究进展及应用[J].硅酸盐学报,2007,35(4):531-536.LI V C.Progress and application of engineered cementitious composites[J].Journal of the Chinese Ceramic Society,2007,35(4):531-536(in Chinese).[2]㊀NAAMAN A E.A statistical theory of strength for fiber reinforced concrete[D].Cambridge:Massachusetts Institute of technology,1972.[3]㊀CHANVILLARD G,RIGAUD plete characterization of tensile properties of ductal UHPFRC according to the French recommendations[C]//High Performance Fiber Reinforced Cement Composites(HPFRCC-4),RILEM Publications SARL,Pro.2003,30:95-113.[4]㊀LI V C.On engineered cementitious composites(ECC)[J].Journal of Advanced Concrete 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